Question

△BCD ​ is dilated to become triangle △B′C′D′.

△BCD has coordinates B(4, 2) , C(6, 2) , and D(6, 5) .

△B′C′D′ has coordinates B′(2, 1) , C′(3, 1) , and D′(3, 2.5) .

What is the scale factor of the dilation?​




0.25

0.5

2

4

Answer 1

when I took the test, it told me that the answer was 0.5

However, they did not explain why

Answer 2

Option B is correct

0.5

Explanation:

The rule of dilation with scale factor k is given by:

`(x, y) \rightarrow (kx, ky)`

As per the statement:

△BCD ​ is dilated to become triangle △B′C′D′

△ BCD has coordinates B(4, 2) , C(6, 2) , and D(6, 5)

△ B′C′D′ has coordinates B′(2, 1) , C′(3, 1) , and D′(3, 2.5)

Apply the rule of dilation on BCD triangle we have;

`B(4, 2) \rightarrow (k(4), k(2)) =B'(4k, 2k)`

B'(2, 1) = B'(4k, 2k)

On comparing both sides we have;

2 = 4k

Divide both sides by 4 we have;

`(2)/(4) = k`

`0.5 = k`

or

k = 0.5

Therefore. the scale factor of the dilation is, 0.5